Preheat oven to 375˚F. Butter the bottom of a 9 x 5 x 3-inch baking dish with your hands.
In a large bowl, whisk whole eggs and yolks, cream, and milk with the ½ cup brown sugar and vanilla extract.
Tear up croissants and mix with egg mixture until well combined.
Spoon half of the egg croissant mixture into the baking dish, sprinkle with dark and white chocolate chips, top with more egg croissant mixture, and finish with remaining chocolate. Sprinkle with 1 tablespoon brown sugar.
Place the dish on a rimmed baking sheet and bake in the oven for 15 to 20 minutes, or until firm to the touch.
Remove from oven. Serve with a dollop of crème fraîche or whipped cream.